Question

Chứng minh : M = 2015 + 2015² + 2015³ + ........+ 2015¹⁰⁰ chia hết cho 2016

Giúp mình với !!!!!!!!!!!!!!!!!!!!!!

Answer 1

\(M=2015+2015^2+...+2015^{100}\)

\(M=\left(2015+2015^2\right)+...+\left(2015^{99}+2015^{100}\right)\)

\(M=2015\left(1+2015\right)+...+2015^{99}\left(1+2015\right)\)

\(M=2015\cdot2016+...+2015^{99}\cdot2016\)

\(M=2016\left(2015+...+2015^{99}\right)⋮2016\)

Answer 2

\(M=2015+2015^2+2015^3+.....+2015^{100}\)
\(=>M=\left(2015+2015^2\right)+\left(2015^3+2015^4\right)+.....+\left(2015^{99}+2015^{100}\right)\)
\(=>M=2015\left(1+2015\right)+2015^3\left(1+2015\right)+2015^{99}\left(1+2015\right)\)
\(=>M=2015.2016+2015^3.2016+.....+2015^{99}.2016\)
\(=>M=\left(2015+2015^3+...+2015^{99}\right).2016⋮2016\)